This invention relates to a PCM decoder for reproducing an audio signal according to the PCM system through the utilization of a consumer cassette video system or one part thereof, and more particularly to an error correcting and controlling system used with such a PCM decoder.
According to the error correcting system for consumer PCM recorders, reproduced analog signals are sampled at sampling times T and converted to digital signals to generate a train of sampled signal words A.sub.0, B.sub.0, A.sub.1, B.sub.1, A.sub.2, B.sub.n, . . . , A.sub.n, B.sub.n, A.sub.n+1, B.sub.n+1, . . . The sampling is alternately effected on a pair of associated channels A and B with the sampling time of the channel B staggered from that of the channel A by one half the sampling time. For each set including six consecutive sampled signal words, one pair of error correcting words P and Q are formed in accordance with the following expressions: EQU P.sub.n =A.sub.n .sym.B.sub.n .sym.A.sub.n+1 .sym.B.sub.n+1 .sym.A.sub.n+2 .sym.B.sub.n+2
and EQU Q.sub.n =T.sup.6 A.sub.n .sym.T.sup.5 B.sub.n .sym.T.sup.4 A.sub.n+1 .sym.T.sup.3 B.sub.n+1 .sym.T.sup.2 A.sub.n+2 .sym.TB.sub.n+2
wherein the symbol .sym. designates the modulo-2-addition, n is a multiple of three (3) and T designates a companion matrix of a polynominal 1+X.sup.8 +X.sup.14 or a Q generating matrix. The Q generating matrix may be expressed by: ##EQU1## Then, the error correcting words P.sub.N and Q.sub.n thus formed are added to the mating set of six sampled signal words to form one data block composed of eight words. The eight words are interleaved and each interleaved word is combined with an error detecting word "CRC" to form a desired word assignment.
It is a common practice to calculate the error value included in data reproduced by the consumer PCM decoder as follows: Syndromes S.sub.1 and S.sub.2, respectively including error correcting words P and Q, are calculated in accordance with EQU S.sub.1 =A.sub.n .sym.B.sub.n .sym.A.sub.n+1 .sym.B.sub.n+1 .sym.A.sub.n+2 .sym.B.sub.n+2 .sym.P.sub.n ( 1)
and EQU S.sub.2 =T.sup.6 A.sub.n .sym.T.sup.5 B.sub.n .sym.T.sup.4 A.sub.n+1 .sym.T.sup.3 B.sub.n+1 .sym.T.sup.2 A.sub.n+2 .sym.TB.sub.n+2 .sym.Q.sub.n ( 2)
By respectively substituting reproduced data r.sub.1, r.sub.2, r.sub.3, r.sub.4, r.sub.5, r.sub.6, r.sub.7, and r.sub.8 for A.sub.n, B.sub.n, A.sub.n+1, B.sub.n+1, A.sub.n+2, B.sub.n+2, P.sub.n and Q.sub.n in the expressions (1) and (2), ##EQU2## result, wherein a modulo-2-addition is effected.
Now assuming that in one data block a single error word exists at a error position i, where i.ltoreq.i.ltoreq.6, EQU S.sub.1 =e.sub.i ( 5)
and EQU S.sub.2 =T.sup.7-i e.sub.i ( 6)
Thus, e.sub.1 =S.sub.1 results. The error position i included in any data block can be generally located through the cyclic redundancy check which is abbreviated as "CRC".
Then, assuming that a data block respectively includes two error words at positions i and j, where i&lt;j and 1.ltoreq.i&lt;j.ltoreq.6, EQU S.sub.1 =e.sub.i .sym.e.sub.j ( 7)
and EQU S.sub.2 =T.sup.7-i e.sub.i .sym.T.sup.7-j e.sub.j ( 8)
result. By solving the expressions (7) and (8) with respect to e.sub.j and e.sub.i, EQU e.sub.j =(I.sym.T.sup.i-j).sup.-1 (S.sub.1 .sym.T.sup.i-7 S.sub.2)=M.sub.k (S.sub.1 .sym.T.sup.i-7 S.sub.2) (9)
and EQU e.sub.i =S.sub.1 .sym.e.sub.j ( 10)
are obtained, wherein I designates a unit matrix. Here M.sub.k =(I.sym.T.sup.i-j).sup.-1 has five combinations of j and i with k=j-i and therefore, five M.sub.k 's are generally stored in an associated memory.
For 1.ltoreq.i.ltoreq.6 and j=7, one obtains EQU S.sub.1 =e.sub.i .sym.e.sub.7 ( 11)
and EQU S.sub.2 =T.sup.7-i e.sub.i ( 12)
and accordingly, EQU e.sub.i =T.sup.i-7 S.sub.2 ( 13)
results.
Also, for 1.ltoreq.i.ltoreq.6 and j=8, one obtains EQU S.sub.1 =e.sub.i ( 14)
and EQU S.sub.2 =T.sup.7-i e.sub.i .sym.e.sub.8 ( 15)
Therefore, EQU e.sub.1 =S.sub.1 ( 16)
results.
The technology and expressions as described above and as will be described later are described in detail, for example, in "STC-007, CONSUMER USE PCM ENCODER-DECODER", June 1976 Electronic Industries Association of Japan and in the A. M. Patel and S. J. Hong article entitled "Optimal Rectangular Code for High Density Magnetic Tapes", IBM JOURNAL OF RESEARCH DEVELOPMENTS, November 1974, pages 579 to 588. The pertinent portions of these references are incorporated by reference herein.
In a conventional error correcting device, reproduced data has been supplied to a first adder circuit and a P register so as to be converted into a syndrome S.sub.1 through a modulo-2-addition. The calculated syndrome S.sub.1 has been stored in the P register. Also, a first multiplier circuit multiplies the reproduced data by a multiplier T.sup.-7 and then a second adder circuit, a second multiplier circuit and Q register which stores a syndrome S.sub.2 are used to calculate T.sup.i-7 S.sub.2 with an error position i supplied from a control circuit for calculating error positions i, j and k=j-i from the reproduced data after the "CRC". The calculated T.sup.i-7 S.sub.2 has been added to the syndrome S.sub.1 from the P register and then multiplied by M.sub.k in a third multiplier circuit, resulting in the calculation of the expression (9). Furthermore, a fourth adder circuit has added the syndrome S.sub.1 from the P register to a product from the third multiplier, whereupon the expression (10) has been calculated.
The error position e.sub.i or error positions e.sub.i and e.sub.j thus calculated have been delivered to an output terminal or terminals assigned thereto and a correcting means has corrected an error word or words followed by the addition thereof to the reproduced data.
Conventional error correcting devices such as that described above have been disadvantageous in that an error or errors can not be detected and corrected in the case where the CRC has missed a single error word or in the case where a dropout compensating circuit is operated to replace more than one data block in video tape recorders.
Also, when the CRC detects not less than three error words in a data block, those error words can not be corrected. Under these circumstances, the control circuit might deliver a control signal to its assigned output terminal. That control signal has performed concealing operations such as the mean value interpolation, holding of the preceding word etc. Thus, when the control circuit detects one error word in a data block and the CRC has missed other error words, the error word is erroneously corrected, thereby resulting in the generation of clicks.
Accordingly, it is an object of the present invention to provide a new and improved and inexpensive error correcting and controlling system capable of detecting and correcting an error word or words which are missed by the CRC.
It is another object of the present invention to provide a new and improved error correcting and controlling system which is most suitable to the video tape recorder and which can correct an error that a dropout compensating circuit involved replaces entirely more than one data block.
It is still another object of the present invention to provide a new and improved error correcting and controlling system for causing a control circuit involved to generate a control signal for the concealing operation such as the mean value interpolation and preventing clicks from occurring upon an erroneous correction due to the presence of two error words one of which has been missed upon the CRC.